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Given 2^p=5^k=10^r , express p in terms of k and r

User Mateen
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6 votes

we are given


2^p=5^k=10^r

Let's assume a term


4^p

we can write as


4^p= (2*2)^p


4^p= 2^p*2^p

now, we know that


2^p=5^k=10^r

so, we can replace 2^p


4^p= 5^k *10^r

now, we can solve for p

we can take ln on both sides


ln(4^p)= ln(5^k *10^r)

now, we can use property of log


p*ln(4)= ln(5^k)+ln(10^r)

we can simplify it further


p*ln(4)= kln(5)+rln(10)

we get


p=(kln(5)+rln(10))/(ln(4))................Answer

User SanduniYW
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